as others have said most helmets absorb impact by crushing the polystyrene. This is rarely accomplished without any cracking. The purpose of the outer shell is to both hold the pieces together and to allow the helmet to slide on most impacting surfaces rather than snag on it (which might well cause a neck injury). The straps also help hold everything together and onto your head; it is currently popular to arrange the straps differently to this but straps that loop over substantial bits of the polystyrene seem to work very well.
Perhaps most importantly with this type you can see if the whole helmet is compromised or not, whereas if the strap disappears into the polystyrene, possibly attached to some kind of internal structure that you cannot see, there is no way of knowing if that is just about to fall apart or not.
FWIW helmets are a lot cheaper than heads are; binning a £15 'daily use' helmet after a few years/knocks is no big deal. Years ago helmets were more expensive and I didn't have two beans to rub together; thus when I broke a helmet I did once patch it up. It was an early microshell helmet. The polystyrene was slightly crushed in once place, cracked through in some other places, and the microshell was cracked in one or two spots.
I reasoned that the crushing wasn't too bad ( about 85% of the original thickness remained) and probably another impact wouldn't occur in the same place anyway. The cracked polystyrene pieces I glued back together using PVA glue. The cracked microshell was 'repaired' using self adhesive tape. I only had to tape around the edges of the microshell (it was taped at this point from new, I just used wider tape) but I'd have happily run duct tape over parts of the shell if the cracks had been more extensive. Probably taping the microshell is a good idea anyway (provided the adhesive doesn't attack and weaken the plastic); if the shell itself cracks a reinforced tape will hold it together.
I used this helmet for run-of-the-mill uses for some time after it had been 'repaired'; I didn't mind leaving it locked to the bike etc because I figured that it owed me nothing. I didn't have cause to 'test it' but it stayed in one piece as well or better than it would have otherwise.
I am pretty sure that the PVA glue poses no problems; to test this I broke pieces of polystyrene, glued them back together and broke them again. They never broke again at the glue line. If I wanted to improve such a helmet (where the microshell wasn't 100% bonded to the top) I'd probably excavate grooves in the outside of the polystyrene shell and glue nylon shot cord into the grooves and then replace the microshell; this would hold the helmet together better than the microshell alone. More modern helmets have the microshell bonded all over so I don't think you could do quite the same thing.
If you want a helmet that will take daily knocks, (and don't mind the extra weight not to mention the looks of the thing), there is something to be said for a hardshell helmet. Skateboard helmets, the Old Bell V1, and some others are like this. Basically if the shell isn't cracked, the polystyrene liner is in more or less one piece, and the straps are still secure, the helmet ought to work OK. With a lot of more modern helmets they are damaged more easily and you can't inspect them so easily.